Can you cast Rime Icicle dagger to entangle an enemy for one round with every attack, or not, because you are creating something and not damaging them with a cold spell directly?
Rime Spell (Metamagic)
Creatures damaged by your spells with the cold descriptor become entangled.Benefit: The frost of your cold spell clings to the target, impeding it for a short time. A rime spell causes creatures that takes cold damage from the spell to become entangled for a number of rounds equal to the original level of the spell.
This feat only affects spells with the cold descriptor. A rime spell uses up a spell slot one level higher than the spell's actual level.
ICICLE DAGGER
School conjuration (creation) [cold]; Level sorcerer/wizard 1, summoner 1, witch 1
Casting Time 1 standard action
Components V, S
Range 0 ft.
Effect one icicle
Duration 1 minute/level
Saving Throw none; Spell Resistance no
You create a masterwork dagger out of ice. The dagger deals 1 point of cold damage in addition to normal dagger damage. If the dagger leaves your hand for more than 1 round, it melts and the spell ends. At 6th level, the dagger functions as a +1 frost dagger. At 11th level, it gains the returning property when thrown, melting away and reforming in your hand just before your next turn.
Well, it would justify the existence of the spell.
Can't see a reason why it wouldn't. It is a spell with the [cold] descriptor, and it does cold damage... only argument might be that it creates a dagger, and the dagger is doing the cold damage - but seeing as how almost all cold attack spells are Conjuration (creation) [cold], they all 'create and object that then causes the damage'.
In the end, you're looking at a feat + 2nd level spell to do slightly more than dagger damage + entangle (a level 1 spell effect)... not that significant, so why not allow it?
Rime Spell says that "[t]he frost of your cold spell clings to the target, impeding it for a short time." So I suppose you could argue that it wouldn't work here since the Icicle Dagger spell doesn't have the Target descriptor.
But that reasoning would mean that it also wouldn't work with Cone of Cold, Ice Storm, a Fireball cast as a Cold spell using the Water Elemental Bloodline Arcana, etc., and I think most people accept that it does work with those spells. So I think most people are interpreting the word 'target' in a less technical sense.